Characteristic path-based colon segmentation

ABSTRACT

This document discusses, among other things, systems and methods for efficiently calculating a colon segmentation from one or more candidate virtual three-dimensional objects. A sequence of image scans are analyzed and regions that represent air-filled objects and tagged-stool are identified as candidate segments. A characteristic path is generated for each candidate segment. The paths are joined using a cost network and re-oriented to be consistent with a typical flythrough path. The connected path is then used to generate a continuous volumetric virtual object.

TECHNICAL FIELD

This patent document pertains generally to volumetric imaging ofbiological or other objects, and more particularly, but not by way oflimitation, to systems or methods to quickly construct athree-dimensional representation of a colon using volumetric imagingdata.

BACKGROUND

In recent years, medical imaging has become a highly valuable tool formedical professionals. One common imaging technique is computedtomography (CT). The CT images, typically of one or more axialvolumetric scans, are either analyzed individually by a radiologist oralternatively, they can be reconstructed into a three-dimensional (3D)model. Three-dimensional modeling has been used in a variety of clinicalapplications including virtual colonoscopies, virtual bronchoscopies,and virtual angioscopies. Using a computer-generated model from CTscans, a radiologist can pre-screen patients for cancer or otherdiseases. Using such a virtual model avoids subjecting the patient to atraditional manual endoscopy, which can be uncomfortable, expensive, andinaccurate.

There are several methods used to construct a volumetric representationof an object, such as when given a set of two-dimensional scans. Themost common method is segmentation. Segmentation uses the imageintensity of portions of a scan to determine what portions are “inside”the object to be defined, and what portions are “outside.” The output ofsuch a segmentation process is a volumetric virtual object, which istypically represented by a collection of voxels (3D pixels) arranged in3D space.

In a typical scan, organs, bone, and other materials appear with varyingintensities along with the region of interest. For example, in a colonicscan, the lower portions of the lungs, the stomach, and the small boweltypically appear. To reduce the processing complexity, it is desirableto isolate the region of interest (e.g., the colon) and remove theexcess portions (e.g., extracolonic components) from the scan.

Some of the same heuristics used in the segmentation to determine theinterior and exterior of a virtual object can be reused to determinerelevant and irrelevant regions in a scan. Image intensity and othercharacteristics such as position and size can be used to help determinerelevant regions.

However, determining all of the relevant regions is made more difficultin many cases where the colon is represented as several disconnectedfragments. In one instance, this can occur when there is insufficientdistention of the colon, which is caused typically by suboptimalinflation. Other causes include large polyps or lesions, which candisconnect adjoining segments of the colon.

SUMMARY

While manual identification of relevant regions in a scan is possible,it is desirable to achieve the identification and combination ofdisconnected fragments automatically. This document discusses, amongother things, systems and methods for efficiently and automaticallycalculating a colon segmentation from one or more candidate virtualthree-dimensional objects. A sequence of image scans are analyzed andregions that represent air-filled objects and tagged-stool areidentified as candidate segments. A characteristic path is generated foreach candidate segment. The paths are joined using a cost network andreoriented to be consistent with a typical flythrough path. Theconnected path is then used to generate a continuous volumetric virtualobject.

Certain examples describe a computer-assisted method of using volumetricimage data to construct a representation of a virtual colon. In suchexamples, the method includes determining a set of one or more candidatesegments in the volumetric image data. Landmark segments are identifiedfrom the set of candidate segments. A characteristic path is generatedfor each candidate segment. A first combined path is created byconnecting the characteristic paths with the use of a cost network. Thefirst combined path is evaluated to determine if it is well-formed. Ifit is well-formed, then the first combined path is used to determine aset of one or more connecting segments between one or more successivepairings of characteristic paths along the first combined path. If thefirst combined path is not well-formed, then a descending colon segmentis identified and the first combined path is recalculated with thedescending colon segment included. The new re-calculated first combinedpath is used to determine a set of one or more connecting segmentsbetween one or more successive pairings of characteristic paths alongthe path. In either case, after the combined path is determined, a setof one or more path segments that correlate to a set of one or morecharacteristic paths that define the combined path is identified. Afinal characteristic path is computed using the set of path segments inunion with the set of connecting segments.

Systems and computer-readable media for performing the methods are alsodescribed. This summary is intended to provide an overview of certainsubject matter of the present patent application. It is not intended toprovide an exclusive or exhaustive explanation of the invention. Thedetailed description is included to provide further information aboutthe subject matter of the present patent application.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, which are not necessarily drawn to scale, like numeralsdescribe substantially similar components throughout the several views.Like numerals having different letter suffixes represent differentinstances of substantially similar components. The drawings illustrategenerally, by way of example, but not by way of limitation, variousembodiments discussed in the present document.

FIG. 1 is a schematic view of a medical scanner, an image storagedevice, and one or more image processing stations.

FIG. 2 is a schematic view of an exemplary image processing station.

FIG. 3 is a schematic view of a system used to calculate acharacteristic path.

FIG. 4 is a flowchart illustrating generally the process of calculatinga combined three-dimensional object from one or more fragments.

FIG. 5 is a flowchart illustrating generally the process of determiningabdominal regions of interest.

FIG. 6 is a flowchart illustrating generally the process of orientingthe rectum and cecum characteristic paths.

FIG. 7 is a planar view of a set of voxels with varying imageintensities.

FIG. 8 is a schematic view of three orthogonal planes with reference tohuman anatomy.

FIG. 9 is a schematic view of a biological image slice.

DETAILED DESCRIPTION

The following detailed description includes references to theaccompanying drawings, which form a part of the detailed description.The drawings show, by way of illustration, specific embodiments in whichthe invention may be practiced. These embodiments, which are alsoreferred to herein as “examples,” are described in enough detail toenable those skilled in the art to practice the invention. Theembodiments may be combined, other embodiments may be utilized, orstructural, logical and electrical changes may be made without departingfrom the scope of the present invention. The following detaileddescription is, therefore, not to be taken in a limiting sense, and thescope of the present invention is defined by the appended claims andtheir equivalents.

In this document, the terms “a” or “an” are used, as is common in patentdocuments, to include one or more than one. In this document, the term“or” is used to refer to a nonexclusive or, unless otherwise indicated.Furthermore, all publications, patents, and patent documents referred toin this document are incorporated by reference herein in their entirety,as though individually incorporated by reference. In the event ofinconsistent usages between this document and those documents soincorporated by reference, the usage in the incorporated reference(s)should be considered supplementary to that of this document; forirreconcilable inconsistencies, the usage in this document controls.

Introduction

The present inventors have recognized that frequently, because ofinsufficient inflation or other causes, a colon in a scan is oftenrepresented as several disconnected fragments. Among other things, thisdocument describes an accurate way to automatically combine fragmentedsegments to form a continuous virtual 3D object using paths. Examples ofa path include, without limitation, centerline paths or characteristicpaths. A characteristic path may not provide complete centricity of theobject and, therefore, does not necessarily constitute a centerline.Nevertheless, a characteristic path will typically be sufficientlyrepresentative of the object to permit full segmentation. Examples of afragmented object include a colon and a small bowel. In this detaileddescription, the process of automatically reconstructing a colonsegmentation is described. However, a similar process could be used forreconstructing segmentations representing a small bowel or othergenerally tubular organs.

FIG. 1 illustrates an example of a system that may use thischaracteristic path data. In this example, a patient 100 is scanned by atypical medical imaging scanner 102. Examples of a medical imagingscanner 102 include, without limitation, a CT scanner and a magneticresonance imaging (MRI) scanner. The scanner 102 is typically connectedto a storage system 106, such as by a data pathway 104. The data pathway104 is typically a local area network (LAN) and the storage system 106is typically an image server. In this example, the storage system 106 isconnected to one or more image processing stations 110A, 10B, 110C, . .. , 110N, by a second data pathway 108, which is typically a LAN.

FIG. 2 illustrates a typical image processing station 110. In thisexample, the image processing station 110 includes one or more inputdevices 410, such as a mouse 200 and a keyboard 202, one or more outputdevices 412, such as a display 204 and a printer 206, and a control unit208, which may include a processor, a local memory, and additionalhardware to control communication between internal and external devices.The image processing station computes a segmentation using the imagesstored at the storage system 106. The segmentation separates the datarepresenting an object of interest (e.g., a colon) from other nearbyobjects represented in the data, such as by using image intensity orother information to make such distinctions. A user can use an imageprocessing station 110 to perform a method that includes generating acomplete segmentation of a disconnected colon using characteristicpaths. One example of this method is discussed below.

EXAMPLES

FIG. 3 illustrates portions of a system 110 that is capable of automaticassembly of one or more segments that represent a colon. In thisexample, a processor 300 is connected to interact with a memory 302. Awide array of possible processor and memory combinations are available.Processors 300 may include commercial units (e.g. Pentium, Motorola68000 series, PowerPC) or specialized units made for use in specificapplications. The memory 302 can include any memory, such assolid-state, magnetic, or optical media.

A user-interface 308 is typically connected to the processor-memorycombination 306. This user-interface 308 typically includes an inputdevice 310 and an output device 312. The input device 310 can be one ormore of a keyboard, a mouse, a touchpad, a microphone, a sensing device,a monitoring device, or any other type of device that allows a computerto receive commands and input data from a user. The output device 312can include such things as a monitor, a printer, a speaker, or any othertype of device that allows a system to represent resultant data to theuser.

In one example, a user can input a command with an input device 310 thatobtains a series of axial scans. The scans are then used by theprocessor-memory combination 306 to create a segmentation of the colon.

First, areas in the scans with low contrast are identified and separatedby Air Mask Extraction module 314. Then, any areas with a high contrastare identified and separated in the Tagged Stool Extraction module 316.The Landmark Identification module 318 determines one or more landmarksegments (e.g., the rectum and cecum). Then, characteristic paths aregenerated for all segments in the abdomen by the Characteristic PathGeneration module 320. The paths are connected by the Path Connectionmodule 322 and then merged in the Path Merger module 324. Finally, a newcharacteristic path is generated using the completely merged andcontinuous colon segmentation by the Post-processing module 326. Then,in one example, the results are displayed on the output device 312 forthe user.

Determining the Set of Candidate Segments

FIG. 4 is a flowchart illustrating an example of a method 400 forautomatically calculating a complete colon segmentation from one or moresegments. At 402, candidate segments, those that are likely portions ofthe colon, are identified and separated. In one example, this isperformed by first finding all regions that represent external air, thenidentifying any regions that represent the lungs or the scanner table,and finally, subtracting these regions from the domain of all air-likevoxels in the volume. This process will typically produce regions thatrepresent abdominal air. In addition, any stool that has been identifiedwill be included as part of the abdominal air region. The regions thatare the result of this process are identified as candidate segments.

Air Mask Extraction

FIG. 5 is a flowchart illustrating an example of a method 402 fordetermining a set of candidate segments. At 500, a mask containing theabdominal air, M_(abd), is extracted. First, M_(ext), a mask containingthe external air surrounding a patient is extracted. In this example,one or more seeds are chosen from extreme x and y positions in theboundary planes of the voxel space. These seeds are used in aregion-growing technique to determine the external air mask.

FIG. 7 illustrates a thresholded region-growing process. For simplicity,a volumetric voxel space 700 is reduced to two dimensions forillustration. A seed voxel 702 is chosen and a threshold is defined (notshown). Typically, the threshold is a maximum or minimum allowable imageintensity. In general, the space or volume is grown from the seed voxel702 by adding adjacent voxels that are over or under the thresholdintensity. This process is continued until all adjacent voxels that areover or under the threshold intensity are included. In this example, thethreshold defines a maximum intensity. So, in the first iteration of theregion-growing process, voxels that are adjacent to the seed voxel 702and have a sufficiently low intensity values (e.g., 704A, 704B, 704C)such that they do not exceed the threshold value are added to a currenttotal voxel space. Adjacent voxels that exceed the threshold (e.g.,706A, 706B) are not added to the voxel space. In the second iteration,voxels that are adjacent to the current total voxel space are evaluatedand those that are under the threshold (e.g., 708A, 708B, 708C) areadded, whereas those that exceed the threshold (e.g., 710A, 710B, 710C)are ignored. This process is continued until all voxels underconsideration in a certain iteration exceed the threshold value.

In this example, when calculating M_(ext), the image intensitythreshold, τ_(ext), is chosen to be relatively lax. In general, it isassumed that a substantially thick layer of intermediate intensities(e.g., skin and clothes) border the external air volumes. Thus there isnot much likelihood of including regions that represent internal airpocket in M_(ext). One example uses τ_(ext)=−324 Hounsfield Units (HU,where 0 HU is the radiodensity of distilled water and −1000 HU is theradiodensity of air) with a sample space along a k×k regular grid, wherek=5·2^(2-R), where R is a constant that corresponds to the currentspatial sampling rate of the volumetric data. In this example, aResolution Ratio (RR) is used to describe the level of sampling. TheResolution Ratio RR1 is the highest resolution with every voxelrepresented, RR2 is one half of RR1 resolution, and RR4 is one fourth ofRR1 resolution. The constant R is then defined as R=2 for RR4, R=1 forRR2, and R=0 for RR1. Typically, using a larger sample space providesfor faster extraction of the external air mask.

FIG. 8 illustrates the three planes that define a volumetric scan inthis context. The illustration depicts a patient's body 800 in theconventional orientation. The sagittal plane 802 is the median plane ofthe body or any plane parallel to it, which divides the body into right(i.e., proximal) and left (i.e., distal) parts. The sagittal plane 802is defined by the y-axis 810 and the z-axis 812. The coronal plane 804is a plane that divides the body into a forward (i.e. anterior) and back(i.e., posterior) parts. The coronal plane 804 is defined by the x-axis808 and the z-axis 812. The axial or transverse plane 806 is a planeperpendicular to the sagittal plane 802 and the coronal plane 804 anddivides the body into a top (i.e., superior) and bottom (i.e., inferior)parts. The axial plane 806 is defined with the x-axis 808 and the y-axis810.

After the external air is segmented, the patient's lungs and possiblythe scanner table are identified in M_(lt), a mask containing the lungsand table. In this example, to find the lungs, the top-most slice (e.g.,the axial slice with the highest z value or the most superior slice) ischosen and thresholded region growing is performed on all voxels thatare not part of the external air mask. In one example, the maximum imageintensity threshold is defined as τ_(lt)=−500 HU, which is morerestrictive than the external air threshold because of the possibleclose proximity of the lungs to the colon, but relaxed enough to allowthe process to permeate the extents of the lungs. In this example,boundaries are defined such that the growing region cannot extend belowsome inferior slice. This accounts for the cases when a portion of thecolon was included in the most superior slice. In one example, theinferior threshold slice is computed as ⅔ of the overall axial span ofthe volume.

The scanner table is typically also detected using the most superiorslice. In this example, if there exists a region that spans more thanhalf the x-span of the volume, it is considered a part of the table andis added to the M_(lt), mask. FIG. 9 illustrates an exemplary axial scanshowing several internal air-filled regions (e.g., 900A, 900B, 900C) andthe table 902. By convention, the axial plane is defined by the x 808and y 810 axes. In this illustration, the table 902 spans more than halfof the x-span of the volume and can typically be confidently identifiedas the table as no other object has similar characteristics.

Once any regions that represent the lung, table, and external air voxelshave been identified, the mask of the abdominal air, M_(abd), isextracted as the complement of all air-like voxels in the volume withthe two masks, M_(ext) and M_(lt). In this example, to determine themask of all air-like voxels, M_(air), a relatively strict threshold,τ_(air)=−825 HU, is used. In general, this can be represented byM_(air)={v|I(v)≦τ_(air)}, where v is a voxel in the mask M_(air) andI(v) is the intensity of a voxel measured in Hounsfield Units. Althoughthis strict threshold potentially disconnects or excludes portions ofthe colon altogether, the strictness prevents false connections betweenthe large and small bowel, as well as inappropriate connections of thecolon to itself. Optionally, an adaptive threshold could be used, suchas one based on the specific characteristics of a particular scan.

Tagged Stool Extraction

In some cases, a patient may be administered a high-contraststool-tagging agent, such as barium sulfate or ionic iodine solution, aspart of their preparation for a virtual colonoscopy. When this occurs,such high-contrast stool voxels in the volume should be included in theregion of interest (e.g., the colon). At 502, tagged-stool is identifiedand extracted. In this example, a mask of high-contrast voxels isgenerated from the volume. This mask, M_(tag), uses a threshold ofτ_(tag)=276 HU, and can be defined as M_(tag)={v|I(v)≧τ_(tag)}, where vis a voxel in the mask M_(tag) and I(v) is the intensity of a voxelmeasured in Hounsfield Units. However, the relatively high intensityvalues of bone results in the inclusion of the spine, lower ribcage, andpelvis among the tagged-stool candidate voxels. To separate thetagged-stool from these bone regions, as well as from other possibleregions with high intensity, the high-intensity regions are analyzedwith respect to the previously obtained air-filled regions.

In particular, in this example, high-intensity regions that share asurface, which is mostly flat, with a previously identified air-filledregion, and that have normals pointing in the coronal direction (i.e., asurface plane that is parallel to the ground when the patient is lyingdown), are considered likely to be liquid stool that is settled adjacentto air and their volumes are merged. To find these adjacent regions,first, surface meshes are computed for both the air and the stoolvolumes. In this example, the surface meshes are created by a marchingcubes technique, which defines a triangular surface mesh. After themeshes are formed, patches of triangles are selected from the air maskwhose normals point positively along the coronal axis (negatively in thecase of a prone scan). These patches are considered candidates ofinterfaces between air and liquid stool. Voxels are selected from thesurface mesh triangles that compose the intersection and are used asseeds for growing regions. At 504, the areas that define theintersection and the mask that defines the tagged stool, M_(tag), areadded to the mask M_(abd), the collection of all voxels representingabdominal air. The result is an augmented mask M_(abd), which definesthe set of candidate segments.

Enumerating Connected Segments

At 404, the candidate segments in the M_(abd) are indexed and, for eachsegment, certain volumetric statistics are calculated and stored. Inthis example, each segment is determined by successive region growing inM_(abd) until all voxels in M_(abd) have been visited. In one example, aminimum voxel volume is imposed to filter out “dust” segments—those thatare insignificant. In this example, the minimum voxel volume is set as10·8^(2−R). The remaining segments S₁, S₂, . . . , S_(i) are thenanalyzed and each segment's volumetric statistics, which include thebounding box {(x _(i), y _(i), Z _(i)), ( x _(i), y _(i), z _(i))} andvoxel distance-to-surface map D(S_(i)), are calculated and stored. Thedistance-to-surface map D(S_(i)) is calculated by assigning each voxelin a segment a value equal to the shortest distance to a surface. Oncethe bounding boxes and distance-to-surface maps for all segments havebeen computed, the volumetric statistics are normalized to the interval[0,1] using a linear transformation.

Identifying Landmark Segments

At 406, the segments' volumetric statistics are analyzed to identifylandmark segments. In this example, the landmark segments of interestare the rectum segment and the cecum segment. In other examples, thelandmark segments of interest may include the descending colon, thetransverse colon, or other identifiable portions of the colon. To findthe landmark segments, certain generalized anatomical knowledge istypically used to create probability functions.

In general, the rectum is positioned at low axial values (toward thebottom of the torso) and high coronal values (toward the back of thetorso). These characteristics are represented by a low z _(i) value anda high y _(i) value. The rectum is also typically less tubular and morevoluminous than other abdominal chambers and therefore some interiorvoxels should have a relatively high distance-to-surface value. Finally,the rectum is typically positioned in the lower axial region, whichallows the search to be refined by only considering the lower half ofthe volumetric representation. Combining these characteristics, the mostlikely rectum segment S_(rect) can be computed as the maximization of:

${f_{rect}(i)} = {\left( {1.0 - {\underset{\_}{z}}_{i}} \right) + {\overset{\_}{y}}_{i} + {\max\left\{ {{d_{j} \in {D\left( S_{i} \right)}}❘{z_{j} \leq {\frac{1}{2}\dim_{z}}}} \right\}}}$

The cecum segment can be found using a similar process. The cecum istypically positioned at low sagittal values (toward the patient's rightside). This can be represented with a low x _(i) value. It is alsotypically more voluminous than other abdominal chambers. Thus, theinterior voxels should exhibit a relatively high distance-to-surfacevalue. Finally, because the cecum is typically positioned toward thepatient's right side, the method 400 can be tuned by restricting thesearch to the lower sagittal range. Thus, using these characteristics,the most likely cecum segment S_(cec) can be computed as themaximization of:

${f_{cec}(i)} = {\left( {1.0 - {\underset{\_}{x}}_{i}} \right) + {\max\left\{ {{d_{j} \in {D\left( S_{i} \right)}}❘{x_{j} \leq {\frac{1}{2}\dim_{x}}}} \right\}}}$

At 408, the segments S_(rect) and S_(cec) are compared and if they referto the same segment, then the method 400 deems that the colon isrepresented as a single segment of M_(abd).

Generating Characteristic Paths and Orienting the Paths

At 410, a characteristic path P_(i) is generated for each coloncandidate segment S_(i). In one example, for each segment, the path isgenerated by first generating a surface mesh over the virtual volume.Then, a reference triangle in the surface mesh is calculated and used asthe starting point for generating distance values for all triangles onthe mesh. After every triangle has been assigned a distance value, oneor more distance values are grouped to form “rings” around the virtualvolume. The centroids of these rings are calculated and used to form acharacteristic path. Examples of generating a characteristic path aredescribed in commonly assigned Samuel W. Peterson U.S. patentapplication Ser. No. 11/273,938 entitled SURFACE-BASED CHARACTERISTICPATH GENERATION, which was filed on Nov. 15, 2005, and which isincorporated by reference herein in its entirety, including itsdescription of examples of generating characteristic paths.

Thus, a characteristic path is defined by a sequence of two or morepoints in 3D space. Generally, a path begins at the first point in thesequence (i.e., the start point) and continues until the last point inthe sequence (i.e., the end point). This sequencing gives a path anorientation or alignment. Optional post-processing may be used to pruneand smooth the resulting path. Other examples may use thinning, distancemaps, or other techniques to generate characteristic paths representingthe colon candidate segments.

At 412, once a path for each colon candidate segment S_(i). iscalculated, the paths that represent the landmark segments S_(rect) andS_(cec) are oriented to be consistent with a particular desiredflythrough direction (e.g., from the rectum to the cecum). FIG. 6 is aflowchart illustrating an example of orienting landmark paths. In thisexample, the starting point of the path in S_(rect) is computed using aweighted function that reflects the normal anatomy. In general, thetypical flythrough path originates at the anus, thus the initial seed islocated in a very low region (a small z value) and toward the rear ofthe patient (a positive y value). Thus, in one example, the initial seedpoint for the rectum segment can be calculated by finding the maximumof:rect(y,z)=−y _(scale) ·y−ω _(z) ·z _(scale) ·zwhere ω_(z), is a weight, in this example ω_(z)=10. The y_(scale) andz_(scale) are provided by the particular scanner and are used to makethe voxel space isotropic.

The characteristic path of S_(rect) is generated from the initial seedpoint. 600, the method 400 can quickly and correctly orient the paththrough the rectum P_(rect) by assigning the initial seed point (or theendpoint of the calculated path that is nearest to the initial seedpoint) the beginning of P_(rect).

However, because the shape of the cecum can vary significantly amongscans and because the characteristic path's starting end is chosenarbitrarily, the path through the cecum P_(cec) may not be orientedconsistent with the desired flythrough path. To correctly orientP_(cec), the method 400 typically uses a combination of generalizedanatomical knowledge and specific volumetric statistics. In thisexample, the shape of the cecum segment is analyzed using a multi-stepmethod and depending on one or more categorizations of the shape, theorientation of the path P_(cec) may be adjusted.

First, at 602, the segment S_(cec) is analyzed to see if it spans asufficient sagittal distance. In this case, the sagittal distance ismeant as the direction normal to the sagittal plane (e.g., the x-axis).In one example, a sufficient sagittal distance is 50% of the totalsagittal distance of M_(abd). Using a relatively large percentage as thethreshold provides a higher probability that the cecum segment, whichwill likely include the transverse colon segment, is properlyidentified. At 604, if S_(cec) spans a sufficient sagittal distance, thepath P_(cec) is oriented such that the point with the maximum x valueprecedes the point with the minimum x value.

At 606, if S_(cec) does not span a sufficient sagittal distance, thenS_(cec) is analyzed to see if it spans a sufficient axial distance. Inthis case, the axial distance is meant as the direction normal to theaxial plane (e.g., the z-axis). In one example, a sufficient axialdistance is 20% of the total axial distance Of M_(abd). At 608, ifS_(cec) spans a sufficient axial distance, then P_(cec) is oriented suchthat the point with the maximum z value is the start of the path.

At 610, if it is determined that S_(cec) does not span a sufficientsagittal distance and does not span a sufficient axial distance, thenthe method 400 orients P_(cec) based on its projection of itscharacteristic path onto the sagittal plane. In some cases, the hepaticflexure folds the colon in front of itself in the sagittal plane (behinditself from the patient's perspective), so the path P_(cec) is orientedsuch that it sweeps out a clockwise path in the sagittal projection.

Connecting Characteristic Paths

At 414, two or more characteristic paths are connected to form acomplete path that starts at the rectum and ends at the cecum. In thisexample, the path that must be found begins at the end of P_(rect) andterminates at the beginning of P_(cec).

A cost network is constructed for the search. In general, whenconsidering two segments, where each is not the rectum or cecum, movingfrom one segment's characteristic path P_(i) to another segment'scharacteristic path P_(j) can be accomplished in four ways (e.g., fromthe start of P_(i) to the start of P_(j); from the start of P_(i) to theend of P_(j); from the end of P_(i) to the start of P_(j); and from theend of P_(i) to the end of P_(j)). Each of these distances arerepresented as a local cost and a total cost. In certain examples, thelocal cost function c_(loc)(i,j)=the linear distance from the end ofP_(i) to the start of P_(j) and the total cost function C_(tot)(i,j)=thesquared distance from the end of P_(i) to the start of P_(j). Thus, thecost network provides a graph with the source node as the starting pointof the path (e.g., the end of P_(rect)), each internal node representsendpoints that the could occur next in the path, and a destination nodethat represent the final endpoint (e.g., the start of path through thececum P_(cec)). Each edge that connects two nodes has a cost associatedwith it, which in this example is total cost (the squared distancebetween two points).

Various methods can be used to determine an optimal solution in a graphor tree structure. In certain examples, a search based on abranch-and-bound technique is used to determine a minimum path fromP_(start) to P_(end) (e.g., P_(rect) and P_(cec)). Several methods basedon the branch-and-bound technique can be used to search a cost tree. Inone example, a branching search is used. In general, a branching searchrecursively divides the search space into smaller regions in a searchfor a solution. This approach can be used in combination with dynamicprogramming. Other examples may use a bounding method to search a costtree. One example of a bounding method defines an upper bound and prunesany regions of a search tree that has a cost that exceeds the upperbound. The result is a pruned search tree with paths that do not exceedthe global threshold. Other examples may use traditional depth-first orbreadth-first searches in an attempt to find a solution. Thebranch-and-bound methods may be used in combination with the traditionalmethods.

In this example, an upper boundary defining a maximum local and totalcost is used to limit the search space. The maximum local cost isinitially set to maximum of the distance from the end of the rectumsegment to the start of the cecum segment or 5% of M_(abd)'s boundingbox's diagonal span. The maximum total cost is the square of thedistance from the end of the rectum segment to the start of the cecumsegment. The search of the cost network is then performed using athresholded depth-first search in one or more iterations until asolution is found. After each unsuccessful iteration, the maximum localcost is incremented, such as at intervals of 5% of the diagonal span ofthe bounding box of M_(abd) until it exceeds an upper boundary. In thisexample, the upper boundary is defined as the distance from the end ofthe rectum segment to the start of the cecum segment. Consequently, ifthe initial maximum local cost is set at this distance, there will onlybe one iteration of the search. In certain examples, the maximum totalcost value can also be incrementally increased to some threshold value.As a natural side-effect of the cost-minimization process, the segmentsthat produced characteristic paths, but were not part of the colon, areautomatically excluded. The final result of the search is a sequence ofpaths {P_(rect), P₁, P₂, . . . , P_(cec)}, which reflects acorresponding sequence of segments {S_(rect), S₁, S₂, . . . , S_(cec)}.The sequence of paths is reoriented to reflect the typical flythroughdirection from rectum to cecum. In certain examples, the sequence ofpaths is used to assist a flythrough of a disconnected colonicsegmentation by transporting a user's viewpoint from the end of onesegment to the beginning of the next based on the sequence of thecorresponding paths.

Recalculating a New Path

At 416, a final path, which is a sequence of characteristic paths, isanalyzed to see if it is well-formed. In this example, the test forwhether the final path is well-formed includes two factors: the totalpath length and the average x value of the entire path. In this example,the total path length is compared to the sum of the x, y, and z lengthsof the path's boundary box. Specifically, in this example, if the totallength of the colon path is not greater than 140% of the sum of thedimensional lengths, then the path is considered not well-formed (i.e.,a major portion is missing). Another factor in determining whether thepath is well-formed is the average x value of the entire calculatedcharacteristic path. The descending colon typically resides on apatient's left side. When a patient is scanned the descending colon'sposition typically contributes a large proportion of positive x value tothe average x value. Thus, if the average x value too low, this exampleassumes that the descending colon was excluded from the characteristicpath and so the path is not well-formed. In this example, a normalized xvalue (e.g., the average x value divided by the span of x in thebounding box) of −0.008 is used as the threshold value. For the path tobe considered well-formed, in this example, the path must pass bothtests. If the path is considered not well-formed, the descending colonis identified and forcibly included in the total characteristic path.

To include the descending colon, first, at 418, when the path isdetermined to be erroneous, the method 400 identifies a descending colonsegment S_(desc). In this example, a descending colon segment S_(desc)is identified as a segment of M_(abd) that has the greatest number ofaxial slices in which it is the maximal sagittal (left-most from thepatient's perspective) segment.

Because every candidate segment had an associated characteristic pathgenerated, the segment S_(desc) already has a characteristic pathP_(desc) generated from a previous step. The orientation of this path ischecked and is adjusted, if necessary, such that the point with theminimum z value is the start of the path. This orientation is consistentwith a typical flythrough path.

At 420, a new sequence of paths is determined using a cost network and abranch-and-bound technique. In this example, to forcibly include thedescending colon segment, the search will determine a first minimum pathfrom P_(rect) to P_(desc) and a second minimum path from P_(desc) toP_(cec), excluding the segments used in the P_(rect)-P_(desc) path. Thefinal path is the combination of these two minimum paths from P_(rect)to P_(cec). The final path, which is a sequence of characteristic paths,is reoriented to reflect the typical flythrough direction from rectum tocecum. As described above, the sequence of paths can be used to assist aflythrough of a disconnected colonic segmentation.

In certain examples, a well-formed final path is used to determine theset of relevant and non-relevant segments in the segmentation. Thesegments that have characteristic paths that make up the well-formedpath are considered colonic, with everything else consideredextra-colonic.

Merging Segments

At 422, the sequence of paths {P_(rect), P₁, P₂, . . . , P_(cec)} aremerged. A fusion mask F_(i), which defines the segments that connect thesequence of paths is calculated. Given a path P_(i) and a successivepath P_(i+1), in the sequence of paths, let c_(i) be the end point ofthe path P_(i) and c_(i+1) be the start point of P_(i+1). Initially,there is an implied straight-line connection between c_(i) and c_(i+1).While the straight-line connections could be used to form the finalcharacteristic path, these type of connections are not representative ofthe actual colonic structure. In order produce a better representation,the method 400 analyzes image intensities in a bounded region to find aprobable connecting segment.

In one example, the merging is performed using Djikstra's path search.For example, when connecting two paths P_(i) and P_(i+1), a cost networkbased on the voxel intensities in the original volume is used. To reduceprocessing, a minimization search can alternatively consider voxelintensity ranges. In this example, the image intensities are ordered byincreasing intensity into groups with a size of 50 HU, starting with allvoxels in M_(air) in the first group. Thus, the first grouping would bedefined by the interval [−1024 HU, −825 HU], the second grouping definedby the interval [−825 HU, −775 HU], the second grouping defined by theinterval [−775 HU, −725 HU], and so on. Alternatively, if a stooltagging agent was used, the voxels in the mask M_(tag) are included inthe first group and all other voxels are grouped according to theirintensity difference from one half of the sum of the threshold of airregions τ_(air) and the threshold of tagged stool regions τ_(tag). Inthis example, τ_(tag)=276 HU and τ_(air)=−825, so½(τ_(air)+τ_(tag))=½(−825+276)=−274.5 HU. Thus, the first grouping wouldbe defined by those voxels with intensities less −825 HU and thosevoxels in the tagged mask. The second grouping would be defined asvoxels with intensities −274.5±25 HU. The next grouping would be definedas those voxels with intensities in the intervals [−299.5 HU, −324.5 HU]and [−249.5 HU, −224.5 HU], and so on.

In one example, for faster execution, the search is limited to be withina radius of 3·2^(2-R) voxels of the bounding box formed by the end ofP_(i) to the start of P_(i+1). To establish the bounding box, letc_(i)=(x_(i), y_(i), z_(i)) be the end point of the path P_(i) andc_(i+1)=(x_(i+1), y_(i+1), z_(i+1)) be the start point of P_(i+1). Thenthe bounding box is defined as {(min(x_(i), x_(i+1)), min(y_(i),y_(i+1)), min(z_(i), Z_(i+1))), (max(x_(i), x_(i+1)), max(y_(i),y_(i+1)) max(z_(i), z_(i+1)))}. In this example, using Djikstra's pathsearch typically results in a single voxel-wide path. In order to ensurean adequate connection, this path is dilated by one voxel. Each path inthe sequence is connected in a similar manner and the collection ofvolumetric segments that connect these paths make up the fusion maskF_(i). The final connected colon segmentation mask is then

$S = {\left( {\overset{k}{\bigcup\limits_{i = 0}}\; S_{i}} \right)\bigcup{\left( {\underset{i = 0}{\bigcup\limits^{k - 1}}F_{i}} \right).}}$Post-processing

At 424, one or more post-processing steps could be performed using thefinal segmentation. In one example, a new characteristic path iscomputed using the final colon segmentation mask S. A new triangularsurface mesh is computed using the complete colon segmentation S and thecharacteristic path is computed by using the rectum point as thereference triangle. The characteristic path is then generated using themethod previously discussed. In another example, the final segmentationis used for display purposes. The entire segmentation alone or incombination with representations of intermediate steps (e.g.,characteristic paths, connecting paths or segments, original data) canbe displayed on one or more output devices. In yet another example, thefinal segmentation is used during a flythrough to keep track of unseenareas within the segmentation.

It is to be understood that the above description is intended to beillustrative, and not restrictive. For example, the above-describedembodiments (and/or aspects thereof) may be used in combination witheach other. Many other embodiments will be apparent to those of skill inthe art upon reviewing the above description. The scope of the inventionshould, therefore, be determined with reference to the appended claims,along with the full scope of equivalents to which such claims areentitled. In the appended claims, the terms “including” and “in which”are used as the plain-English equivalents of the respective terms“comprising” and “wherein.” Also, in the following claims, the terms“including” and “comprising” are open-ended, that is, a system, device,article, or process that includes elements in addition to those listedafter such a term in a claim are still deemed to fall within the scopeof that claim. Moreover, in the following claims, the terms “first,”“second,” and “third,” etc. are used merely as labels, and are notintended to impose numerical requirements on their objects.

The Abstract of the Disclosure is provided to comply with 37 C.F.R.§1.72(b), requiring an abstract that will allow the reader to quicklyascertain the nature of the technical disclosure. It is submitted withthe understanding that it will not be used to interpret or limit thescope or meaning of the claims. In addition, in the foregoing DetailedDescription, various features may be grouped together to streamline thedisclosure. This method of disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter may lie in less thanall features of a single disclosed embodiment. Thus the following claimsare hereby incorporated into the Detailed Description, with each claimstanding on its own as a separate embodiment.

1. A computer-assisted method of using volumetric image data toconstruct a representation of a virtual organ, the method comprising:determining, using one or more computers, a set of one or more candidatesegments in the volumetric image data; identifying, using the one ormore computer, a set of one or more landmark segments from the set ofcandidate segments; computing, using the one or more computer, acharacteristic path for each segment in the set of candidate segments;and creating, using the one or more computer, a first combined path byconnecting the characteristic paths, wherein the connecting is performedusing a cost network; orienting, using the one or more computer, thecharacteristic paths for the one or more candidate segments to beconsistent with a start point and an end point, wherein the candidatesegment is a cecum segment, and wherein orienting the associatedcharacteristic path comprises: if the cecum segment spans a sufficientsagittal distance, then orienting the path such that an endpoint with amaximum x value precedes an endpoint with a minimum x value; if thececum segment spans a sufficient axial distance, then orienting the pathsuch that an endpoint with a maximum z value is the start of the path;if the cecum segment does not span a sufficient sagittal distance or asufficient axial distance, then orienting the path by: projecting thepath onto a sagittal plane to create a sagittal projection; andorienting the path such that it represents a clockwise path in thesagittal projection.
 2. A computer-assisted method of using volumetricimage data to construct a representation of a virtual organ, the methodcomprising: determining, using one or more computer, a set of one ormore candidate segments in the volumetric image data; identifying, usingthe one or more computer, a set of one or more landmark segments fromthe set of candidate segments; computing, using the one or morecomputer, a characteristic path for each segment in the set of candidatesegments; and creating, using the one or more computer, a first combinedpath by connecting the characteristic paths, wherein the connecting isperformed using a cost network; determining if the first combined pathis well-formed; if the first combined path is well-formed, then:reorienting each characteristic path in the first combined path to beconsistent with a flythrough direction; and using the first combinedpath to determine a set of one or more connecting segments between oneor more successive pairings of characteristic paths along the firstcombined path.
 3. The method of claim 2, wherein the using the firstcombined path to determine one or more connecting segments includesconnecting the end of a first characteristic path with the beginning ofa second characteristic path using a straight line.
 4. The method ofclaim 2, wherein using the first combined path to determine one or moreconnecting segments includes performing a Djikstra's path search fromthe end of a first characteristic path to the beginning of a secondcharacteristic path.
 5. The method of claim 2, comprising traversing afragmented virtual three-dimensional object using the first combinedpath.
 6. The method of claim 2, comprising identifying a set of relevantsegments using the first combined path.
 7. The method of claim 2,comprising identifying a set of non-relevant segments using the firstcombined path.
 8. The method of claim 2, comprising: identifying a setof one or more path segments that correlate to a set of one or morecharacteristic paths that define the first combined path; andcalculating a final segmentation, wherein the final segmentation is theunion of the set of path segments and the set of connecting segments. 9.The method of claim 8, comprising computing a final characteristic pathusing the final segmentation.
 10. The method of claim 8, comprisingusing the final segmentation to determine a group of zero or more unseenregions of the final segmentation.
 11. A computer-assisted method ofusing volumetric image data to construct a representation of a virtualorgan, the method comprising: determining, using one or more computer, aset of one or more candidate segments in the volumetric image data;identifying, using the one or more computer, a set of one or morelandmark segments from the set of candidate segments; computing, usingthe one or more computer, a characteristic path for each segment in theset of candidate segments; and creating, using the one or more computer,a first combined path by connecting the characteristic paths, whereinthe connecting is performed using a cost network; determining if thefirst combined path is well-formed; if the first combined path is notwell-formed, then: identifying a descending colon segment; recalculatingthe first combined path to include the descending colon segment;reorienting each characteristic path in the first combined path to beconsistent with a flythrough direction; and using the first combinedpath to compute a set of one or more connecting segments between one ormore successive pairings along the first combined path.
 12. The methodof claim 11, wherein the identifying the descending colon segmentincludes using one or more specified anatomical characteristics.
 13. Themethod of claim 11, comprising traversing a fragmented virtualthree-dimensional object using the first combined path.
 14. The methodof claim 11, comprising: identifying a set of one or more path segmentsthat correlate to a set of one or more characteristic paths that definethe first combined path; and calculating a final segmentation, whereinthe final segmentation is the union of the set of path segments and theset of connecting segments.
 15. The method of claim 14, comprising usingthe final segmentation to compute a final characteristic path.
 16. Themethod of claim 15, wherein the computing the final characteristic pathcomprises: generating a triangular surface mesh; choosing a referencetriangle from a set of all triangles in the triangular surface mesh;generating a relative distance value of every triangle in the set of alltriangles in the triangular surface mesh in relation to the referencetriangle; grouping triangles to form rings that approximatecross-sectional circumferences of the final segmentation along alongitudinal axis of the segmentation; calculating centroids of therings; and connecting the centroids of the rings to form the finalcharacteristic path.
 17. The method of claim 16, comprising: pruning thefinal characteristic path to remove branches shorter than a thresholdlength; and smoothing the final characteristic path.
 18. Acomputer-assisted method of using volumetric image data to construct arepresentation of a virtual organ, the method comprising: determining,using one or more computer, a set of one or more candidate segments inthe volumetric image data; identifying, using the one or more computer,a set of one or more landmark segments from the set of candidatesegments; computing, using the one or more computer, a characteristicpath for each segment in the set of candidate segments; and creating,using the one or more computer, a first combined path by connecting thecharacteristic paths, wherein the connecting is performed using a costnetwork; wherein the determining the set of one or more candidatesegments comprises: identifying a set of one or more low-contrastregions in the volumetric image data; identifying a set of one or morerelevant low-contrast regions from the set of low-contrast areas;identifying a set of one or more high-contrast regions in the volumetricimage data; identifying a set of one or more relevant high-contrastregions from the set of high-contrast areas; and computing the set ofone or more candidate segments by forming a union of the set of relevantlow-contrast regions with the set of relevant high-contrast regions. 19.The method of claim 18, wherein a relevant high-contrast region istagged stool.
 20. The method of claim 18, wherein identifying a set ofone or more relevant high-contrast regions comprises: computing one ormore surface meshes for each high-contrast region; selecting one or moregroups of triangles that form planes which are parallel to the coronalplane; selecting one or more voxels associated with the one or moregroups of triangles; and using the one or more voxels to grow regionsthat represent tagged-stool regions.
 21. The method of claim 18, whereinthe identifying the set of one or more landmark segments comprises usingone or more anatomical characteristics to identify each landmarksegment.
 22. A computer-assisted method of using volumetric image datato construct a representation of a virtual organ, the method comprising:determining, using one or more computer, a set of one or more candidatesegments in the volumetric image data; identifying, using the one ormore computer, a set of one or more landmark segments from the set ofcandidate segments; computing, using the one or more computer, acharacteristic path for each segment in the set of candidate segments;and creating, using the one or more computer, a first combined path byconnecting the characteristic paths, wherein the connecting is performedusing a cost network; wherein the computing a characteristic path foreach segment comprises: generating a triangular surface mesh; choosing areference triangle from a set of all triangles in the triangular surfacemesh; generating a relative distance value of every triangle in the setof all triangles in the triangular surface mesh in relation to thereference triangle; grouping triangles to form rings that approximatecross-sectional circumferences of the segment along a longitudinal axisof the segment; calculating centroids of the rings; and connecting thecentroids of the rings to form the characteristic path.
 23. The methodof claim 22, comprising: pruning the characteristic path to removebranches shorter than a threshold length; and smoothing thecharacteristic path.
 24. The method of claim 22, wherein thedetermining, the identifying, the computing, and the creating areperformed automatically without user intervention.
 25. Acomputer-assisted method of using volumetric image data to construct arepresentation of a virtual organ, the method comprising: determining,using one or more computer, a set of one or more candidate segments inthe volumetric image data; identifying, using the one or more computer,a set of one or more landmark segments from the set of candidatesegments; computing, using the one or more computer, a characteristicpath for each segment in the set of candidate segments; and creating,using the one or more computer, a first combined path by connecting thecharacteristic paths, wherein the connecting is performed using a costnetwork; wherein creating a first combined path comprises: selecting astart and end point; constructing the cost network, wherein the costnetwork includes a source node that represents the start point, zero ormore internal nodes representing possible connecting points, adestination node representing the end point, and one or more edges thatconnect pairs of nodes where each edge is associated with a cost; andsearching the cost network to find a path with a minimum cost.
 26. Themethod of claim 25, wherein the searching includes using abranch-and-bound technique.
 27. The method of claim 25, wherein thesearching includes using a depth-first search.
 28. A computer-readablemedium including instructions that, when performed by a computer, usesvolumetric image data to construct a representation of a virtual colonby: determining a set of one or more candidate segments in thevolumetric image data; identifying a set of one or more landmarksegments from the set of candidate segments; computing a characteristicpath for each segment in the set of candidate segments; and creating afirst combined path by connecting the characteristic paths, wherein theconnecting is performed using a cost network; determining if the firstcombined path is well-formed; and if the path is not well-formed, then:identifying a descending colon segment; recalculating the first combinedpath to include the descending colon segment; reorienting eachcharacteristic path in the first combined path to be consistent with aflythrough direction; and using the first combined path to compute a setof one or more connecting segments between one or more successivepairings along the first combined path.
 29. The computer-readable mediumof claim 28, wherein the identifying the descending colon segmentincludes instructions for using one or more specified anatomicalcharacteristics.
 30. The computer-readable medium of claim 28,comprising instructions for: identifying a set of one or more pathsegments that correlate to a set of one or more characteristic pathsthat define the first combined path; and calculating a finalsegmentation, wherein the final segmentation is the union of the set ofpath segments and the set of connecting segments.
 31. Thecomputer-readable medium of claim 30, comprising instructions forcomputing a final characteristic path using the final segmentation. 32.A computer-readable medium including instructions that, when performedby a computer, uses volumetric image data to construct a representationof a virtual colon by: determining a set of one or more candidatesegments in the volumetric image data; identifying a set of one or morelandmark segments from the set of candidate segments; computing acharacteristic path for each segment in the set of candidate segments;and creating a first combined path by connecting the characteristicpaths, wherein the connecting is performed using a cost network; whereinthe computing a characteristic path for each segment comprisesinstructions for: generating a triangular surface mesh; choosing areference triangle from a set of all triangles in the triangular surfacemesh; generating a relative distance value of every triangle in the setof all triangles in the triangular surface mesh in relation to thereference triangle; grouping triangles to form rings that approximatecross-sectional circumferences of the structure along a longitudinalaxis of the structure; calculating centroids of the rings; andconnecting the centroids of the rings to form the characteristic path.33. A computer-readable medium including instructions that, whenperformed by a computer, uses volumetric image data to construct arepresentation of a virtual colon by: determining a set of one or morecandidate segments in the volumetric image data; identifying a set ofone or more landmark segments from the set of candidate segments;computing a characteristic path for each segment in the set of candidatesegments; and creating a first combined path by connecting thecharacteristic paths, wherein the connecting is performed using a costnetwork, wherein creating a first combined path comprises instructionsfor: determining a start and end point; constructing the cost network,wherein the cost network includes a source node that represents thestart point, zero or more internal nodes representing possibleconnecting points, a destination node representing the end point, andone or more edges that connect pairs of nodes where each edge isassociated with a cost; and searching the cost network to find a pathwith a minimum cost.
 34. A system for using volumetric image data toconstruct a representation of a virtual colon, the system comprising: aprocessor, operable to perform a calculation to combine two or morecharacteristic paths, wherein each path represents a colon segment, andwherein the calculation uses a cost network, the cost network includinga source node that represents a start point, zero or more internal nodesrepresenting possible connecting points, a destination node representingan end point, and one or more edges that connect pairs of nodes whereeach edge is associated with a cost; a memory, coupled to the processor,the memory operable for storing data; and a user-interface that permitsa user to store and retrieve information from the memory using theprocessor, wherein the processor computes the characteristic paths foreach colon segment by: generating a triangular surface mesh; choosing areference triangle from a set of all triangles in the triangular surfacemesh; generating a relative distance value of every triangle in the setof all triangles in the triangular surface mesh in relation to thereference triangle; grouping triangles to form rings that approximatecross-sectional circumferences of the colon segment along a longitudinalaxis of the structure; calculating centroids of the rings; andconnecting the centroids of the rings to form the characteristic path.35. The system of claim 34, wherein the processor uses the memory toprovide a complete representation of a virtual colon to theuser-interface.
 36. A system for using volumetric image data toconstruct a representation of a virtual colon, comprising: a processorcoupled to a memory; a user-interface coupled to the processor; an airmask extraction module to run on the processor to identify a set of oneor more relevant low-contrast segments in a volumetric image data andstore in the memory; a tagged stool extraction module to run on theprocessor to identify a set of one or more relevant high-contrastsegments in the volumetric image data and store in the memory; alandmark identification module to run on the processor to determine oneor more landmark segments in the union of the set of relevantlow-contrast segments and the set of relevant high-contrast segmentsreceived from memory; a characteristic path generation module to run onthe processor to calculate a characteristic path for each segment in theunion of the set of relevant low-contrast segments and the set ofrelevant high-contrast segments received from memory; a path connectionmodule to run on the processor to connect two or more characteristicpaths to form a first combined characteristic path and store in thememory; a path merger module to run on the processor to calculate one ormore connecting segments that bridge segments represented by the firstcombined characteristic path and store in the memory; a post-processingmodule to run on the processor to use the connecting segments and thesegments represented by the first combined characteristic path to form afinal combined characteristic path and store in the memory.
 37. Thesystem of claim 36, wherein the characteristic path generation modulecalculates each characteristic path by: generating a triangular surfacemesh; choosing a reference triangle from a set of all triangles in thetriangular surface mesh; generating a relative distance value of everytriangle in the set of all triangles in the triangular surface mesh inrelation to the reference triangle; grouping triangles to form ringsthat approximate cross-sectional circumferences of the colon segmentalong a longitudinal axis of the structure; calculating centroids of therings; and connecting the centroids of the rings to form thecharacteristic path.
 38. The system of claim 36, wherein the pathconnection module connects characteristic paths using a cost network anda minimization process, wherein the cost network includes a source nodethat represents a start point, zero or more internal nodes representingpossible connecting points, a destination node representing an endpoint, and one or more edges that connect pairs of nodes where each edgeis associated with a cost, and wherein the minimization process includesa branch-and-bound technique.
 39. The system of claim 36, wherein theprocessor uses the memory to provide a representation of a virtual colonto the user-interface.